Multigrid methods for parabolic distributed optimal control problems
Journal of Computational and Applied Mathematics
A Multigrid Scheme for Elliptic Constrained Optimal Control Problems
Computational Optimization and Applications
Journal of Computational and Applied Mathematics
Efficient Preconditioners for Optimality Systems Arising in Connection with Inverse Problems
SIAM Journal on Control and Optimization
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We present a finite difference multigrid technique that efficiently solves optimal control problems associated with the steady state solid fuel ignition model. This is a nonlinear indefinite problem which gives rise to singular optimal control systems. Regarding the direct problem, necessary and sufficient conditions for existence of solutions are given and second-order convergence of numerical solution errors with respect to the mesh size is proven. A robust nonlinear multigrid method is implemented to validate this convergence estimate.Two optimal control strategies for solid fuel ignition phenomena are considered and compared. The corresponding optimality systems are solved to second-order accuracy by a multigrid method whose convergence properties are independent of the values of the weights in the cost functionals and of the number of grid points.